Conics of Hyperbole

Conics of Hyperbola

Introduction

A conic is a plane curve which can be plotted on a cone of revolution of two sheets (Dawes, 1974). After position it occupies in relation to a cone a plane that intersects it will determine an intersection:

A circle the plane is perpendicular to the axis;

An ellipse: the plane is inclined to the axis, but it does not cut one of the two sheets;

A hyperbola: the plane is inclined or parallel to the axis and intersects the two plies;

A parable plane is parallel to a tangent plane to the cone.

Hyperbola

The hyperbola is the set of points in a plane which differs from distances from two fixed points called foci is a constant amount: 2a (Weidner, 1992).

Although it is not easy to find objects in the form of hyperbole, this curve is important because it is necessary to explain certain phenomena: the inverse proportionality, Boule Mariotte law, etc (Dawes, 1974).

In the following diagram a view of constructed hyperbola is highlighting the layouts and elements of it.

Elements of the hyperbola

In the hyperbola distinguish the following elements:

The radius vector of a point P is the segments PF and PF '.

The focal axis is the line through the foci F and F '.

The shaft is the segment bisector F'F.

The center of the hyperbola is the point O at which the axes intersect. It is the center of symmetry. Y axes are axes of symmetry.

The focal distance is F'F segment whose length is 2c.

The vertices are the points A and A ', cutoffs focal axis with the hyperbole and B and B', cutoffs secondary axis with the circle with center A and radius c = OF.

The axis transverse or real axis is the segment AA '.

The shaft does not transverse or imaginary axis is the segment BB '.

Lengths of the shafts

You can see that the real axis then the 2nd AA'made OA = OA '= a

Similarly length is taken as the imaginary axis BB '2b, then OB, OB = '= b.

And the focal length is FF '= 2c.

Relationship between a, b and c

The Pythagorean relationship between these segments is: c 2 = a 2 + b 2.

Eccentricity

Noting several hyperbolas is that some rams are more open than others. This characteristic of being more open or more closed is measured with a number called eccentricity (e) , which is the ratio between to c: e = c / a ...